In magnetoelectric (ME) materials, magnetization and electric polarization may be induced with the application of an electric field and a magnetic field, respectively. Ever since the ME effect was first observed in single phase Cr2O3 (Astrov, D. N., 1961, Soy. Phys.JETP, vol. 13, no. 4, pp. 729-733; and Folen, V. J. et al., 1961, Phys. Rev. Lett., vol. 6, no. 11, pp. 607-608), many other ME materials having high ME coupling coefficient α have been discovered (Ebnabbasi, K. et al., 2012, J. Appl. Phys., vol. 111, no. 7, p. 07C719). In the early stages of development of ME materials, a high ME effect could be observed only at low temperatures, not at room temperature (Srinivasan, G. et al., 2003, Phys. Rev. B, vol. 67, no. 1, p. 014418; and Zhao et al., Sci. Rep., vol. 4, June 2014, Art. no. 5255). At present, ME materials are known which are either single phase or composites consisting of piezoelectric and magnetostrictive laminated layers. These materials produce ME effects at room temperature. In particular, hexaferrite materials, both in single-phase bulk form and as films, exhibit sufficiently high α values that they are suitable for making devices such as sensors, circulators, and phase shifters for use at room temperature (Zare, S. et al., 2015, Appl. Phys. Lett., vol. 106, no. 19, p. 193502; Zare, S. et al., 2015, J. Magn. Magn. Mater., vol. 393, pp. 423-428; Ramesh, R. et al., 2007, Nature Mater., vol. 6, no. 1, pp. 21-29; Fiebig, M., 2005, J. Phys. D, Appl. Phys., vol. 38, no. 8, pp. R123R152; and Zare et al., 2015, J. Appl. Phys., vol. 117, no. 21, p. 214506).
Hexaferrites are a large group of ferrites having a hexagonal crystal structure. Based on their compositions and substructures, they are classified into different types, namely M-, U-, W-, X-, Y-, and Z-type. Both the uniqueness of the composition and the arrangement of substructures in a unit cell of a hexaferrite crystal make one hexaferrite distinguishable from another. For example, an M-type hexaferrite, which has the simplest structure among all the hexaferrites, consists of R and S building blocks (also called spinel blocks) with the arrangement RSR*S* (FIG. 2). R* and S* are the same as R and S, respectively, but rotated by 180° around the c axis. In a Z-type hexaferrite, the arrangement of the blocks is RSTSR*S*T*S*. in which again T* is defined similarly to R* and S*. The composition of the S, R and T spinel blocks are TMFe2O4, BaFe4O7 and 2BaFe4O7, respectively, where TM represents a transition metal ion and Ba may be replaced by Sr or Pb ions. The chemical formula of a typical M-type hexaferrite is BaFe12O19, and those of typical Y- and Z-type hexaferrites are Ba2Fe12TM2O22 and Ba3Fe24TM2O41, respectively, The lattice constants along c-axis in the M-, Y- and Z-type hexaferrites are, 22, 43, and 52 Angstroms, respectively. The Z-type hexaferrites, which have the largest unit cell along the c-axis, have the most spinel blocks (RSTSR*S*T*S*).
In general, the greater the number of spinel blocks, the more difficult it is to prepare the hexaferrite in question since hexaferrite phases other than the one desired may admix with the desired phase. For example, the Z-Type hexaferrite, requiring stacking of the most spinel blocks, is indeed the most difficult to prepare as it readily admixes with M- and U-type hexaferrites at the high temperatures needed for its preparation (Pollert, E., 1985, Progress in crystal growth and characterization, 11(3): p. 155-205; Kohn, J. et al., 1971, Science, 172(3983): p. 519-525; Smit, J. et al., 1959, Ferrites Philips Technical Library. Eindhoven, The Netherlands, p. 157; Beblo, M. et al., 1982, Landolt-Börnstein: Numerical Data and Functional Relationships in Science and Technology-New Series in Landolt-Bornstein: Group 6: Astronomy; Braun P. et al., 1957, Philips Res. Rep, 12: p. 491-548; Albanese, G. et al., 1976, Journal of Physics C: Solid State Physics, 9(7): p. 1313; and Wohlfarth, E. P., Handbook of Magnetic Materials: A Handbook on the Properties of Magnetically Ordered Substances Vol. 2. 1980: Access Online via Elsevier). In the classic M-type hexaferrite (Ba, Sr)Fe12O19, large divalent elements, such as Ba, Pb, and Sr, are located in the R block, where only octahedral sites reside. Only the S block contains tetrahedral sites.
It is a commonly held notion that local distortions or strains induced in the ME hexaferrites due to the replacement of a Ba ion with a smaller Sr ion gives rise to its ME property. This distortion, located in the T block for the Z-type and Y-type hexaferrites, implies that the bonding angle in Fe—O—Fe combination near the Sr substitution is changed from 116° (with Ba) to 123° (with Sr) (Zhao et al., Sci. Rep., vol. 4, June 2014, Art. no. 5255; Wang, L. et al., 2012, Sci. Rep., vol. 2, Art. no. 223; Mohebbi, M. et al., 2013, J Appl. Phys., vol. 113, no. 17, p. 17C710; Tokunaga, Y. et al., 2010, Phys. Rev. Lett., vol. 105, no. 25, p. 257201; Ishiwata, S. et al., 2008, Science, vol. 319, no. 5870, pp. 1643-1646; Hiraoka, Y. et al., 2011, J. Appl. Phys., vol. 110, no. 3, p. 033920; Taniguchi, K. et al., Appl. Phys. Exp., vol. 1, no. 3, p. 031301; Soda, M. et al., 2011, Phys. Rev. Lett., vol. 106, no. 8, p. 087201; and Kitagawa, Y. 2010, Nature Mater, vol. 9, no. 10, pp. 797-802). This change in bonding angle has implications for the super exchange interaction between the two Fe ions, one occupying an octahedral and the other a tetrahedral site. In ferrites, this combination normally represents the strongest exchange interaction between Fe ions, with the potential to enhance the ME effect exhibited by the hexaferrite. Under strain, this interaction is weakened giving rise to a localized anisotropic exchange which results in a potential spin spiral configuration as described by the Dzyaloshinski-Moriya interaction model (I. Dzyaloshinsky, 1958, Journal of Physics and Chemistry of Solids, 4(4): p. 241-255; and T. Moriya, 1960, Physical Review, 1120(1): p. 91).
In addition to the substitution of Ba ions with ions of Sr, some of the Fe ions in a hexaferrite may be substituted by cobalt ions (Miller, A., Landolt-Börnstein: Numerical data and functional relationships in science and technology, Advanced Materials and Technologies, Berlin, Germany: Springer, 2002). Room temperature ME effect in cobalt-substituted M-type hexaferrite SrFe8Ti2Co2O19 has been reported in the bulk (Wang, L. et al., 2012, Sci. Rep., vol. 2, Art. no. 223) as well as in the thin film form of the hexaferrite (Mohebbi, M. et al., 2013, J. Appl. Phys., vol. 113, no. 17, p. 17C710). The change in ME effect brought about by cobalt substitution has been studied in Sr2+Cox2+Ti3−0.5x4+ Fe83+O192− using different amounts of cobalt substituting for iron (Izadkhah, H. et al., 2015, Appl. Phys. Lett., vol. 106, no. 14, p. 142905). This substitution was observed to have a major effect on the value of a measured at room temperature. In the M-type hexaferrite SrFe8Co2Ti2O19, it has been suggested that Co and Ti occupy only octahedral sites, 12k, 2a, and 4f2 (Wang, L. et al., 2012, Sci. Rep., vol. 2, Art. no. 223). Since the Ti substituents occupy 12k sites (see FIG. 2), the spin coupling between the S and R blocks is weakened, inducing a spin spiral configuration. It has been suggested that the spin spiral configuration induced by cobalt ion substitution in both M- and Z-type hexaferrites is responsible for the increased ME effect observed in these hexaferrites. Of note, it is assumed that in cobalt substituted ME hexaferrites, Co ions substitute only in the octahedral sites (T. Moriya, 1960, Physical Review, 1120(1): p. 91).
There is a need for methods of preparing hexaferrites having an enhanced ME effect.